You can use:
<%ifnot auth_no_authentication%>
<%if use_cookie%>
<%if Username and Username ne 'default'%>
<a href="db.cgi?do=search_results&db=jdamembers&&ls=A&col=Company_Name&sb=Company_Name">A</a>
<%else%>
<a href="db.cgi?do=search_results&db=jdamembers&uid=default&ls=A&col=Company_Name&sb=Company_Name">A</a>
<%endif%>
<%else%>
<a href="db.cgi?do=search_results&db=jdamembers&sid=<%session_id%>&ls=A&col=Company_Name&sb=Company_Name">A</a>
<%endif%>
<%endif%>
TheStone.
B.
<%ifnot auth_no_authentication%>
<%if use_cookie%>
<%if Username and Username ne 'default'%>
<a href="db.cgi?do=search_results&db=jdamembers&&ls=A&col=Company_Name&sb=Company_Name">A</a>
<%else%>
<a href="db.cgi?do=search_results&db=jdamembers&uid=default&ls=A&col=Company_Name&sb=Company_Name">A</a>
<%endif%>
<%else%>
<a href="db.cgi?do=search_results&db=jdamembers&sid=<%session_id%>&ls=A&col=Company_Name&sb=Company_Name">A</a>
<%endif%>
<%endif%>
TheStone.
B.